Being out and about on a sick day is usually fine, a worker may do whatever they like on their sick days which contribute to getting healthy again, and what that is is nobody’s business except the worker and their doctors.

To be fired an employee must be warned for the same violation of company policy on three separate occasions within one year before they can be fired. (Eg. faking being sick three times.) Unrelated but reasonable excuses don’t fly, the employee can sue and typically wins.

But of course the detectives are shady about their methods, they’re operating on the knife’s edge of what’s legal.